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2.UNITS AND MEASUREMENTS (1.)The Vander Waal’s equation of state for real gases is given as (P + a V2 ) (V − b) = nRT which of the following terms has dimensions different from that of energy (a.) PV (b.) a V2 (c.) ab V2 (d.) bP (2.)A calorie is a unit of heat and equal 4.2 J. Suppose we employ a system of units in which the unit of mass is αkg, the unit of length is β metre and the unit of time is γ sec. In this new system. 1 calorie = (a.) α −1β −2γ 2 (b.) 4.2αβ 2γ 2 (c.) αβ 2γ 2 (d.) 4.2α −1β −2γ 2 (3.)Which is the correct unit for measuring nuclear radii (a.) Micron (b.) Millimetre (c.) Angstrom (d.) Fermi (4.)The dimensional formula for Boltzmann’s constant is (a.) [ML 2T −2θ −1 ] (b.) [ML 2T −2 ] (c.) [ML 0T −2θ −1 ] (d.) [ML −2T −1θ −1 ] (5.)Newton/metre2 is the unit of (a.) Energy (b.) Momentum (c.) Force (d.) Pressure (6.)Given, Force = α density+ β3 What are the dimensions of α, β? (a.) [ML 2T −2 ],[ML −1/3 ] (b.) [M2L 4T −2 ],[M1/3L −1 ] (c.) [M2L −2T −2 ],[M1/3L −1 ] (d.) [M2L −2T2 ], [ML−3 ] (7.)If the velocity v(is cms−1) of a particle is given in terms of t (in second) by the relation v = at + b t+c then, the dimensions of a, b and c are a b c (a.) [L] [LT] [T 2 ] (b.) [L 2 ] [T] [LT−2 ] (c.) [LT2 ] [LT] [L] (d.) [LT−2 ] [L] [T] (8.)The length l, breadth b and thickness t of a block are measured with the help of a metre scale. Given l = 15.12 ± 0.01cm, b = 10.15 ± 0.01cm, t = 5.28 ± 0.01cm. The percentage error in volume is (a.) 0.64% (b.) 0.28% (c.) 0.37% (d.) 0.48% (9.)If C, R, L and I denote capacity, resistance, inductance and electric current respectively, the quantities having the same dimensions of time are (1) CR (2) L R (3) √LC (4) LI 2 (a.) (1) and (2) only (b.) (1) and (3) only (c.) (1) and (4) only (d.) (1), (2) and (3) only (10.)Which is different from others by units (a.) Phase difference (b.) Mechanical equivalent (c.) Loudness of sound (d.) Poisson’s ratio (11.)Which of the following quantities has the same dimensions as that of energy (a.) Power (b.) Force (c.) Momentum (d.) Work (12.)In the equation y = a sin (ωt + kx,) the dimensional formula of ω is (a.) [M0L 0T −1 ] (b.) [M0LT −1 ] (c.) [ML 0T 0 ] (d.) [M0L −1T 0 ] (13.)The dimensions of time constant are (a.) [M0L 0T 0 ] (b.) [M0L 0T] (c.) [MLT] (d.) None of these (14.)Which unit is not for length (a.) Parsec (b.) Light year (c.) Angstrom (d.) Nano
(15.)1kWh = (a.) 1000 W (b.) 36 × 105 J (c.) 1000 J (d.) 3600 J (16.)Unit of impulse is (a.) Newton (b.) kg − m (c.) kg − m/s (d.) Joule (17.)The physical quantity having the dimensions [M−1L −3T 3A 2 ] is (a.) Resistance (b.) Resistivity (c.) Electrical conductivity (d.) Electromotive force (18.)The number of significant figures in the numbers 4.8000 × 104 and 48000.50 are respectively (a.) 5 and 6 (b.) 5 and 7 (c.) 2 and 7 (d.) 2 and 6 (19.)If the time period (T) of vibration of a liquid drop depends on surface tension (S), radius (r) of the drop and density (ρ) of the liquid, then the expression of T is (a.) T = k√ρr3/S (b.) T = k√ρ 1/2r 3/S (c.) T = k√ρr 3/S 1/2 (d.) None of these (20.)Dimensions of potential energy are (a.) MLT −1 (b.) ML 2T −2 (c.) ML −1T −2 (d.) ML −1T −2 (21.)If voltage V = (100 ± 5) volt and current I = (10 ± 0.2) A, the percentage error in resistance R is (a.) 5.2% (b.) 25% (c.) 7% (d.) 10% (22.)The velocity of transverse wave in a string is v = √ T m , where T is the tension in the string and m is mass per unit length. If T = 3.0 kgf, mass of string is 2.5 g and length of string is 1.00m, then the percentage error in the measurement of velocity is (a.) 0.5 (b.) 0.7 (c.) 2.3 (d.) 3.6 (23.)The dimensions of emf in MKS is (a.) [ML −1T −2Q −2 ] (b.) [ML −2T −2Q −2 ] (c.) [MLT −2Q −1 ] (d.) [ML 2T −2Q −1 ] (24.)The physical quantity having the dimensions [M−1L −3A 2 ] is (a.) Resistance (b.) Resistivity (c.) Electrical conductivity (d.) Electromotive force (25.)What is the dimensional formula of planck ′s constant linear momentum ? (a.) [M0L 0T 0 ] (b.) [M0L 0T] (c.) [M0LT 0 ] (d.) [MLT −1 ] (26.)The constant of proportionality 1 4πε0 in Coulomb’s law has the following dimensions (a.) C −2Nm2 (b.) C 2N −1m−2 (c.) C 2Nm2 (d.) C −2N −1m−2 (27.)If force (F), length (L) and time (T) are assumed to be fundamental units, then the dimensional formula of the mass will be (a.) FL −1T 2 (b.) FL −1T −2 (c.) FL −1T −1 (d.) FL 2T 2 (28.)The position of a particle at time t is given by the relation x(t) = ( v0 α ) (1 − e αt), where v0 is constant and α > 0. The dimensions of v0 and α are respectively (a.) M0L 1T −1 and T −1 (b.) M0L 1T 0 and T −1 (c.) M0L 1T −1 and LT −2 (d.) M0L 1T −1 and T (29.)One yard in SI units is equal (a.) 1.9144 metre (b.) 0.9144 metre (c.) 0.09144 kilometre (d.) 1.0936 kilometre (30.)The magnetic force on a point moving charge is F⃗ = q(V⃗ × B⃗ ). Here, q =electric charge V⃗ = velocity of the point charge B⃗ =magnetic field The dimensions of B⃗ (a.) [MLT −1A] (b.) [MLT −2A −1 ]
(c.) [MT −1A −1 ] (d.) None of these (31.)Out of the following four dimensional quantities, which one qualifies to be called a dimensional constant? (a.) Acceleration due to gravity (b.) Surface tension of water (c.) Weight of a standard kilogram mass (d.) The velocity of light in vacuum (32.)In an experiment, the following observation’s were recorded: L = 2.820 m, M = 3.00 kg, l = 0.087 cm, diameter D = 0.041 cm. Taking g = 9.81 m/s 2 using the formula, Y = 4MgL πD2l , the maximum permissible error in Y is (a.) 7.96% (b.) 4.56% (c.) 6.50% (d.) 8.42% (33.)An object is moving through the liquid. The viscous damping force acting on it is proportional to the velocity. Then dimension of constant of proportionality is (a.) ML −1T −1 (b.) MLT −1 (c.) M0LT −1 (d.) ML 0T −1 (34.)Which of the following represents a volt (a.) Joule/second (b.) Watt/ampere (c.) Watt/coulomb (d.) Coulomb/joule (35.)Electric displacement is given by D = εE, Here, ε =electric permittivity E =electric field strength The dimensions of electric displacement are (a.) [ML −2TA] (b.) [L −2T −1A] (c.) [L −2TA] (d.) None of these (36.)Dimensions of luminous flux are (a.) ML 2T −2 (b.) ML 2T −3 (c.) ML 2T −1 (d.) MLT −2 (37.)The fundamental physical quantities that have same dimensions in the dimensional formulae of torque and angular momentum are (a.) Mass, time (b.) Time, length (c.) Mass, length (d.) Time, mole (38.)Dimensions of the following three quantities are the same (a.) Work, energy, force (b.) Velocity, momentum, impulse (c.) Potential energy, kinetic energy, momentum (d.) Pressure, stress, coefficient of elasticity (39.)Dimensions of kinetic energy are (a.) ML 2T −2 (b.) M2LT −1 (c.) ML 2T −1 (d.) ML 3T −1 (40.)A sextant is used to measure (a.) Area of hill (b.) Height of an object (c.) Breadth of a tower (d.) Volume of the building (41.)Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful (a.) A/B (b. ) A + B (c.) A − B (d. ) None (42.)The dimension of 1 2 ε0E 2 , where ε0 is permittivity of free space and E is electric field, is (a.) MLT 1 (b.) ML 2T −2 (c.) ML −1T −2 (d.) ML 2T −1 (43.)Which of the following is the smallest unit (a.) Millimetre (b.) Angstrom (c.) Fermi (d.) Metre (44.)Density of wood is 0.5 gm/cc in the CGS system of units. The corresponding value in MKS units is (a.) 500 (b.) 5 (c.) 0.5 (d.) 5000 (45.)A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is (a.) e2 − e1 (b.) e1 + 2e2 (c.) e1 + e2 (d.) e1 − 2e2 (46.)Length cannot be measured by (a.) Fermi (b.) Debye (c.) Micron
(d.) Light year (47.)[ML 3T −1Q −2 ] is the dimensional formula of (a.) Resistance (b.) Resistivity (c.) Conductance (d.) Conductivity (48.)If the dimensions of a physical quantity are given by MaL bT c , then the physical quantity will be (a.) Pressure if a = 1, b = −1, c = −2 (b.) Velocity if a = 1, b = 0, c = −1 (c.) Acceleration if a = 1, b = 1, c = −2 (d.) Force if a = 0, b = −1, c = −2 (49.)Farad is not equivalent to (a.) q V (b.) qv 2 (c.) q 2 J (d.) J V2 (50.)‘Torr’ is the unit of (a.) Pressure (b.) Volume (c.) Density (d.) Flux (51.)Universal time is based on (a.) Rotation of earth on its axis (b.) Oscillations of quartz crystal (c.) Vibrations of cesium atom (d.) Earth’s orbital motion around the sun (52.)The number of significant figures in all the given numbers 25.12, 2009, 4.156 and 1.217 × 10−4 is (a.) 1 (b.) 2 (c.) 3 (d.) 4 (53.)If C and R represent capacitance and resistance respectively, then the dimensions of RC are (a.) M0L 0 T 2 (b.) M0L 0 T (c.) ML −1 (d.) None of these above (54.)The surface tension is T = F l , then the dimensions of surface tension are (a.) [MLT −2 ] (b.) [MT −2 ] (c.) [M0L 0T 0 ] (d.) None of these (55.)The dimensions of resistivity in terms of M, L, T and Q where Q stands for the dimensions of charge, is (a.) ML 3T −1Q −2 (b.) ML 3T −2Q −1 (c.) ML2T −1Q −1 (d.) MLT −1Q −1 (56.)X = 3YZ 2 find dimension of Y in (MKSA) system, If X and Z are the dimensions of capacity and magnetic field respectively (a.) M−3L −2T −4A −1 (b.) ML −2 (c.) M−3L −2T 4A 4 (d.) M−3L −2T 8A 4 (57.)Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is (a.) 6% (b.) Zero (c.) 1% (d.) 3% (58.)Force constant has the same dimensions as (a.) Coefficient of viscosity (b.) Surface tension (c.) Frequency (d.) Impulse (59.)Taking frequency f, velocity v and density ρ to be the fundamental quantities, then the dimensional formula for momentum will be (a.) [ρv 4f −3 ] (b.) [ρv 3f −1 ] (c.) [ρvf 2 ] (d.) [ρ 2v 2f 2 ] (60.)A unit of area, often used in measuring land areas, is the hectare defined as 104 m2 . An open-pit coal mine consumes 75 hectares of land, down to a depth of 26m, each year. What volume of earth, in cubic kilometre, is removed in this time? (a.) 0.01 (b.) 0.02 (c.) 0.03 (d.) 0.04 (61.)The dimensional formula of 1 ε0 e 2 hc is (a.) [M0L 0T 0A 0 ] (b.) [M−1L 3T 2A] (c.) [ML 3T −4A −2 ] (d.) [M−1L −3T 4 ] (62.)Ampere − hour is a unit of (a.) Quantity of electricity (b.) Strength of electric current (c.) Power (d.) Energy (63.)If L denotes the inductance of an inductor through which a current I is flowing, then the dimensional formula of LI 2 is